Preface Introduction 1 Combinatorial games 1.1 Definition of combinatorial games 1.2 Fundamental theorem of combinatorial games 1.3 Nim 1.4 Hex and other games 1.5 Tree games 1.6 Grundy functions 1.7 Bogus Nim-sums 1.

8 Chapter summary 2 Two-person zero-sum games 2.1 Games in normal form 2.2 Saddle points and equilibrium pairs 2.3 Maximin and minimax 2.4 Mixed strategies 2.5 2-by-2 matrix games 2.6 2-by-n, m-by-2 and 3-by-3 matrix games 2.7 Linear programming 2.

8 Chapter summary 3 Solving two-person zero-sum games using LP 3.1 Perfect canonical linear programming problems 3.2 The simplex method 3.3 Pivoting 3.4 The perfect phase of the simplex method 3.5 The Big M method 3.6 Bland's rules to prevent cycling 3.7 Duality and the simplex method 3.

8 Solution of game matrices 3.9 Chapter summary 4 Non-zero-sum games and k-person games 4.1 The general setting 4.2 Nash equilibria 4.3 Graphical method for 2 Ã-- 2 matrix games 4.4 Inadequacies of Nash equilibria & cooperative games 4.5 The Nash arbitration procedure 4.6 Games with two or more players 4.

7 Coalitions 4.8 Games in coalition form 4.9 The Shapley value 4.10 The Banzhaf power index 4.11 Imputations 4.12 Strategic equivalence 4.13 Stable sets 4.14 Chapter summary 5 Imperfect Information Games 5.

1 The general setting 5.2 Complete information games in extensive form 5.3 Imperfect information games in extensive form 5.4 Games with random effects 5.5 Chapter summary 6 Computer solutions to games 6.1 Zero-sum games - invertible matrices 6.2 Zero sum games - linear program problem (LP) 6.3 Special Linear Programming Capabilities 6.

4 Non-zero sum games - linear complementarity problem (LCP) 6.5 Special game packages 6.6 Chapter summary Appendices Appendix A Utility theory Appendix B Nash's theorem Appendix C Finite probability theory Appendix D Calculus & Differentiation Appendix E Linear Algebra Appendix F Linear Programming Appendix G Named Games and Game Data Answers to selected exercises Bibliography Index.